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A Look at the Descriptional Complexity of SNQ P Systems

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Enjoying Natural Computing

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11270))

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Abstract

We present the known results pertaining to the recently introduced spiking neural P Systems with communication on request (SNQ P Systems). Aside from showing the properties of these systems working with multiple types of spikes (as defined originally) we also give the results obtained by our group in the area of SNQ P Systems using only one type of spikes. All the results are given from the perspective of descriptional complexity, taking into account the number of neurons needed in the universal systems. Several open problems and ideas for improvements of the results are also presented.

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References

  1. Bîlbîe, F.-D., Păun, A.: Universality of SNQ P systems using one type of spikes. In: Proceedings of the 18th International Conference on Membrane Computing (CMC 2017), Bradford, UK, 25–28 July 2017

    Google Scholar 

  2. Carbarle, F.G.C., Adorna, H.N., Pérez-Jiménez, M.J.: Sequential spiking neural P systems with structural plasticity based on max/min spike number. Neural Comput. Appl. 27(5), 1337–1347 (2016)

    Article  Google Scholar 

  3. Chen, H., Freund, R., Ionescu, M., Păun, G., Pérez-Jiménez, M.J.: On string languages generated by spiking neural P systems. Fundam. Inform. 18(6), 1371–1382 (2007)

    MathSciNet  MATH  Google Scholar 

  4. Csuhaj-Varju, E.: Grammar Systems: A Grammatical Approach to Distribution and Cooperation. Gordon and Breach, London (1994)

    MATH  Google Scholar 

  5. Ibarra, O.H., Păun, A., Rodríguez-Patón, A.: Sequential SNP systems based on min/max spike number. Theor. Comput. Sci. 410, 2982–2991 (2009)

    Article  MathSciNet  Google Scholar 

  6. Ionescu, M., Păun, G., Yokomori, T.: Spiking neural P systems. Fundam. Inform. 71(2–3), 279–308 (2006)

    MathSciNet  MATH  Google Scholar 

  7. Ionescu, M., Păun, A., Păun, G., Pérez-Jiménez, M.J.: Computing with spiking neural P systems: traces and small universal systems. In: Mao, C., Yokomori, T. (eds.) DNA 2006. LNCS, vol. 4287, pp. 1–16. Springer, Heidelberg (2006). https://doi.org/10.1007/11925903_1

    Chapter  MATH  Google Scholar 

  8. Korec, I.: Small universal register machines. Theor. Comput. Sci. 168, 267–301 (1996)

    Article  MathSciNet  Google Scholar 

  9. Leporati, A., Mauri, G., Zandron, C., Păun, G., Pérez-Jiménez, M.J.: Uniform solutions to SAT and Subset Sum by spiking neural P systems. Nat. Comput. 8(4), 681–702 (2009)

    Article  MathSciNet  Google Scholar 

  10. Minsky, M.: Computation - Finite and Infinite Machines. Prentice Hall, Englewood Cliffs (1967)

    MATH  Google Scholar 

  11. Pan, L., Păun, G., Zhang, G., Neri, F.: Spiking neural P systems with communication on request. Int. J. Neural Syst. 28(08), 1750042 (2017)

    Article  Google Scholar 

  12. Pan, L., Păun, G., Pérez-Jiménez, M.J.: Spiking neural P systems with neuron division and budding. Sci. China Inf. Sci. 54(8), 1596–1607 (2011)

    Article  MathSciNet  Google Scholar 

  13. Pan, T., Shi, X., Zhang, Z., Xu, F.: A small universal spiking neural P system with communication on request. Neurocomputing 275, 1622–1628 (2018)

    Article  Google Scholar 

  14. Păun, A., Bîlbîe, F.-D.: Universality of SNQ P systems using one type of spikes and restrictive rule application. Int. J. Comput. Sci. (2018, accepted)

    Google Scholar 

  15. Păun, G.: Membrane Computing - An Introduction. Springer, Berlin (2002). https://doi.org/10.1007/978-3-642-56196-2

    Book  MATH  Google Scholar 

  16. Păun, G.: Grammar systems: a grammatical approach to distribution and cooperation. In: Fülöp, Z., Gécseg, F. (eds.) ICALP 1995. LNCS, vol. 944, pp. 429–443. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-60084-1_94

    Chapter  Google Scholar 

  17. Păun, G., Pérez-Jiménez, M.J., Rozenberg, G.: Computing morphisms by spiking neural P systems. Int. J. Comput. Sci. 18(6), 1371–1382 (2007)

    MathSciNet  MATH  Google Scholar 

  18. Păun, G., Pérez-Jiménez, M.J., Rozenberg, G.: Spike trains in spiking neural P systems. Int. J. Found. Comput. Sci. 17(04), 975–1002 (2006)

    Article  MathSciNet  Google Scholar 

  19. Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. 3. Springer, Berlin (1997). https://doi.org/10.1007/978-3-642-59126-6

    Book  MATH  Google Scholar 

  20. Schroeppel, R.: A two counter machine cannot calculate \(2^N\). Technical report AIM-257, A. I. Laboratory, Massachusetts Institute of Technology, Cambridge, MA, 1–31 May 1972. ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-257.pdf. Accessed 14 Oct 2015

  21. Wang, J., Hoogeboom, H.J., Pan, L., Păun, G., Pérez-Jiménez, M.J.: Spiking neural P systems with weights. Neural Comput. 22(10), 1615–2646 (2010)

    Article  MathSciNet  Google Scholar 

  22. Wu, T., Bîlbîe, F.-D., Păun, A., Pan, L., Neri, F.: Simplified and yet Turing universal spiking neural P systems with communication on request. Int. J. Neural Syst. (2018, accepted)

    Google Scholar 

  23. Zhang, G., Rong, H., Neri, F., Pérez-Jiménez, M.J.: An optimization spiking neural P system for approximately solving combinatorial optimization problems. Int. J. Neural Syst. 24(5), 1440006 (2014)

    Article  Google Scholar 

  24. Zeng, X., Pan, L., Pérez-Jiménez, M.J.: Small universal simple spiking neural P systems with weights. Sci. China Inf. Sci. 57(9), 1–11 (2014)

    Article  MathSciNet  Google Scholar 

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Correspondence to Andrei Păun .

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Păun, A., Bîlbîe, FD. (2018). A Look at the Descriptional Complexity of SNQ P Systems. In: Graciani, C., Riscos-Núñez, A., Păun, G., Rozenberg, G., Salomaa, A. (eds) Enjoying Natural Computing. Lecture Notes in Computer Science(), vol 11270. Springer, Cham. https://doi.org/10.1007/978-3-030-00265-7_18

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  • DOI: https://doi.org/10.1007/978-3-030-00265-7_18

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